Atkin-Lehner |
2+ 3+ 5- 17- 31- |
Signs for the Atkin-Lehner involutions |
Class |
47430f |
Isogeny class |
Conductor |
47430 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
17664 |
Modular degree for the optimal curve |
Δ |
-28458000 = -1 · 24 · 33 · 53 · 17 · 31 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -4 1 -5 17- -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-129,653] |
[a1,a2,a3,a4,a6] |
Generators |
[2:19:1] [-11:31:1] |
Generators of the group modulo torsion |
j |
-8831234763/1054000 |
j-invariant |
L |
6.7311565824996 |
L(r)(E,1)/r! |
Ω |
2.0409346610408 |
Real period |
R |
0.27483962417607 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999989 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47430u1 |
Quadratic twists by: -3 |